From the diagram given, we can say that;
BD + DC = BC
BD = BC - DC
Given
BC = 54x - 14
DC = 23x + 83
Substitute the given expressions into the formula as shown;
BD = 54x - 14 - (23x + 83)
BD = 54x - 14 - 23x - 83
BD = 54x - 23x -14 - 83
BD = 31x - 97
Hence the length of BD is 31x - 97
